This paper establishes non-uniform continuity of the data-to-solution map in the periodic case for the two-component Fornberg-Whitham system in Besov spaces $ B^s_{p, r}(\mathbb{T}) \times B^{s-1}_{p, r}(\mathbb{T}) $ for $ s > \max\{2+\frac{1}{p}, \frac{5}{2}\} $. In particular, when $ p = 2 $ and $ r = 2 $, this proves the non-uniform dependence on initial data for the system in Sobolev spaces $ H^s(\mathbb{T})\times H^{s-1}(\mathbb{T}) $ for $ s > \frac{5}{2} $.
Citation: Prerona Dutta, Barbara Lee Keyfitz. Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces[J]. AIMS Mathematics, 2024, 9(9): 25284-25296. doi: 10.3934/math.20241234
This paper establishes non-uniform continuity of the data-to-solution map in the periodic case for the two-component Fornberg-Whitham system in Besov spaces $ B^s_{p, r}(\mathbb{T}) \times B^{s-1}_{p, r}(\mathbb{T}) $ for $ s > \max\{2+\frac{1}{p}, \frac{5}{2}\} $. In particular, when $ p = 2 $ and $ r = 2 $, this proves the non-uniform dependence on initial data for the system in Sobolev spaces $ H^s(\mathbb{T})\times H^{s-1}(\mathbb{T}) $ for $ s > \frac{5}{2} $.
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Prerona Dutta, Barbara Lee Keyfitz. Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces[J]. AIMS Mathematics, 2024, 9(9): 25284-25296. doi: 10.3934/math.20241234
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